Subgroups — #449×D₂₅₁ #44559562

Order 32128.

812 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#41×D₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×SD₁₆×D₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₈×D₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
4	#121×D₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
5	#30631835	C₂	1	1	yes	maximal, characteristic, complemented
6	#30631834	C₂	1	1	yes	maximal, characteristic, complemented
7	#30631833	C₂	1	1	yes	maximal, characteristic, complemented
8	#30631832	C₂	1	1	yes	maximal, characteristic, complemented
9	#30631831	C₂	1	1	yes	maximal, characteristic, complemented
10	#30631830	C₂	1	1	yes	maximal, characteristic, complemented
11	#30631829	C₂	1	1	yes	maximal, characteristic, complemented
12	#103×D₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
13	#102×D₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²⋊C₈×D₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
15	#449×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#16860811	C₂²	1	1	yes	characteristic, complemented
17	C₂×#16860810	—	2	1	no	—
18	C₂×#16860810	C₂²	1	1	yes	characteristic, complemented
19	C₂×#16860809	—	2	1	no	—
20	C₂×#16860809	C₂²	1	1	yes	characteristic, complemented
21	#41×D₂₅₁	—	2	4	no	—
22	#41×D₂₅₁	—	2	4	no	—
23	C₂×Q₈×D₂₅₁	C₂²	1	1	yes	characteristic
24	C₂×D₄×D₂₅₁	—	2	1	no	—
25	C₂×D₄×D₂₅₁	—	2	1	no	—
26	C₂×D₄×D₂₅₁	C₂²	1	1	yes	characteristic
27	C₂×D₄×D₂₅₁	C₂²	1	1	yes	characteristic
28	C₂²×C₄×D₂₅₁	—	2	1	no	—
29	C₂²×C₄×D₂₅₁	C₂²	1	1	yes	characteristic
30	C₂×#16860799	C₂²	1	1	yes	characteristic, complemented
31	C₂×#16860798	C₂²	1	1	yes	characteristic, complemented
32	C₂×#16860797	C₂²	1	1	yes	characteristic, complemented
33	SD₁₆×D₂₅₁	—	2	4	no	—
34	C₂×D₂₀₀₈	C₂²	1	1	yes	characteristic, complemented
35	C₂×#16860795	C₂²	1	1	yes	characteristic, complemented
36	C₂×#16860795	C₂²	1	1	yes	characteristic, complemented
37	D₈×D₂₅₁	—	2	4	no	—
38	C₂×C₈×D₂₅₁	C₂²	1	1	yes	characteristic
39	C₂×C₈×D₂₅₁	C₂²	1	1	yes	characteristic
40	#22548690	C₂²	1	1	yes	characteristic, complemented
41	#22548689	C₂²	1	1	yes	characteristic, complemented
42	#22548688	—	2	1	no	—
43	#22548687	—	2	1	no	—
44	#22548686	C₂²	1	1	yes	characteristic, complemented
45	C₄⋊C₄×D₂₅₁	C₂²	1	1	yes	characteristic
46	C₂²⋊C₄×D₂₅₁	—	2	1	no	—
47	#22548640	C₂²	1	1	yes	characteristic, complemented
48	#22548639	C₂²	1	1	yes	characteristic, complemented
49	#22548638	C₂²	1	1	yes	characteristic, complemented
50	#22548637	C₂²	1	1	yes	characteristic, complemented
51	#22548636	C₂²	1	1	yes	characteristic, complemented
52	#22548635	C₂²	1	1	yes	characteristic, complemented
53	C₂²⋊(C₂₅₁⋊C₈)	C₂²	1	1	yes	characteristic, complemented
54	(C₂×D₂₅₁)⋊C₈	C₂²	1	1	yes	characteristic, complemented
55	(C₂×D₂₅₁)⋊C₈	C₂²	1	1	yes	characteristic, complemented
56	C₂×#41×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
57	C₂×SD₁₆×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
58	C₂×D₈×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
59	#121×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
60	#103×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
61	#102×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
62	C₂²⋊C₈×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
63	C₂³×D₂₅₁	—	2	1	no	—
64	C₂³×D₂₅₁	—	2	1	no	—
65	C₂³×D₂₅₁	D₄	1	1	yes	characteristic
66	#16860811	—	2	2	no	—
67	#16860811	—	2	2	no	—
68	#16860810	—	2	8	no	—
69	#16860810	—	2	2	no	—
70	#16860810	—	2	2	no	—
71	#16860809	—	2	8	no	—
72	#16860809	—	2	2	no	—
73	#16860809	—	2	2	no	—
74	C₂×Dic₅₀₂	—	2	1	no	—
75	C₂×Dic₅₀₂	C₂³	1	1	yes	characteristic
76	Q₈×D₂₅₁	—	2	2	no	—
77	Q₈×D₂₅₁	D₄	1	4	yes	complemented
78	C₂×D₁₀₀₄	—	2	1	no	—
79	C₂×D₁₀₀₄	—	2	1	no	—
80	C₂×D₁₀₀₄	C₂³	1	1	yes	characteristic
81	C₂×D₁₀₀₄	C₂³	1	1	yes	characteristic
82	C₂×C₂²⋊D₂₅₁	—	2	1	no	—
83	C₂×C₂²⋊D₂₅₁	—	2	1	no	—
84	C₂×C₂²⋊D₂₅₁	—	2	1	no	—
85	C₂×C₂²⋊D₂₅₁	—	2	1	no	—
86	C₂×C₂²⋊D₂₅₁	—	2	1	no	—
87	C₂×C₂²⋊D₂₅₁	—	2	1	no	—
88	D₄×D₂₅₁	—	2	8	no	—
89	D₄×D₂₅₁	—	2	2	no	—
90	D₄×D₂₅₁	—	2	2	no	—
91	D₄×D₂₅₁	—	2	2	no	—
92	D₄×D₂₅₁	—	4	4	no	—
93	D₄×D₂₅₁	D₄	1	4	yes	complemented
94	C₂²×Dic₂₅₁	—	2	1	no	—
95	C₂²×Dic₂₅₁	D₄	1	1	yes	characteristic
96	C₂×C₄×D₂₅₁	—	2	8	no	—
97	C₂×C₄×D₂₅₁	—	2	1	no	—
98	C₂×C₄×D₂₅₁	—	2	1	no	—
99	C₂×C₄×D₂₅₁	—	2	2	no	—
100	C₂×C₄×D₂₅₁	—	2	2	no	—
101	C₂×C₄×D₂₅₁	—	2	1	no	—
102	C₂×C₄×D₂₅₁	—	2	1	no	—
103	C₂×C₄×D₂₅₁	D₄	1	1	yes	characteristic
104	C₂×C₄×D₂₅₁	D₄	1	1	yes	characteristic
105	C₂×C₄×D₂₅₁	C₂³	1	1	yes	characteristic
106	C₂×C₄×D₂₅₁	C₂³	1	1	yes	characteristic
107	#16860799	—	2	2	no	—
108	#16860798	—	2	2	no	—
109	#16860797	—	2	2	no	—
110	D₂₀₀₈	—	2	2	no	—
111	#16860795	—	2	2	no	—
112	#16860795	—	2	2	no	—
113	C₂×C₂₅₁⋊C₈	C₂³	1	1	yes	characteristic
114	C₂×C₂₅₁⋊C₈	C₂³	1	1	yes	characteristic
115	C₈×D₂₅₁	—	2	2	no	—
116	C₈×D₂₅₁	—	2	2	no	—
117	C₄⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
118	Dic₂₅₁⋊C₄	—	2	1	no	—
119	C₂²⋊Dic₂₅₁	—	2	1	no	—
120	(C₂×D₂₅₁)⋊C₄	—	2	1	no	—
121	(C₂×D₂₅₁)⋊C₄	—	2	1	no	—
122	#41×C₂₅₁	—	2	2	no	—
123	#41×C₂₅₁	—	2	2	no	—
124	C₂×Q₈×C₂₅₁	C₂³	1	1	yes	characteristic
125	C₂×D₄×C₂₅₁	—	2	1	no	—
126	C₂×D₄×C₂₅₁	—	2	1	no	—
127	C₂×D₄×C₂₅₁	C₂³	1	1	yes	characteristic
128	C₂×D₄×C₂₅₁	C₂³	1	1	yes	characteristic
129	C₂²×C₄×C₂₅₁	—	2	1	no	—
130	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
131	SD₁₆×C₂₅₁	—	2	2	no	—
132	D₈×C₂₅₁	—	2	2	no	—
133	C₂×C₈×C₂₅₁	C₂³	1	1	yes	characteristic
134	C₂×C₈×C₂₅₁	C₂³	1	1	yes	characteristic
135	C₄⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
136	C₂²⋊C₄×C₂₅₁	—	2	1	no	—
137	C₂²×D₂₅₁	—	2	1	no	—
138	C₂²×D₂₅₁	—	2	2	no	—
139	C₂²×D₂₅₁	—	2	4	no	—
140	C₂²×D₂₅₁	—	2	2	no	—
141	C₂²×D₂₅₁	—	2	2	no	—
142	C₂²×D₂₅₁	—	2	1	no	—
143	C₂²×D₂₅₁	—	4	2	no	—
144	C₂²×D₂₅₁	—	4	2	no	—
145	C₂²×D₂₅₁	—	4	2	no	—
146	C₂²×D₂₅₁	—	4	2	no	—
147	C₂²×D₂₅₁	—	4	2	no	—
148	C₂²×D₂₅₁	C₂×D₄	1	1	yes	characteristic
149	C₂²×D₂₅₁	C₂×D₄	1	1	yes	characteristic
150	Dic₅₀₂	—	2	1	no	—
151	Dic₅₀₂	—	2	4	no	—
152	Dic₅₀₂	C₂×D₄	1	2	yes	complemented
153	D₁₀₀₄	—	2	4	no	—
154	D₁₀₀₄	—	2	1	no	—
155	D₁₀₀₄	—	2	1	no	—
156	D₁₀₀₄	—	2	1	no	—
157	D₁₀₀₄	—	4	2	no	—
158	D₁₀₀₄	C₂×D₄	1	2	yes	complemented
159	C₂²⋊D₂₅₁	—	2	4	no	—
160	C₂²⋊D₂₅₁	—	2	4	no	—
161	C₂²⋊D₂₅₁	—	2	4	no	—
162	C₂²⋊D₂₅₁	—	4	2	no	—
163	C₂²⋊D₂₅₁	—	4	2	no	—
164	C₂²⋊D₂₅₁	—	4	2	no	—
165	C₂×Dic₂₅₁	—	2	4	no	—
166	C₂×Dic₂₅₁	—	2	1	no	—
167	C₂×Dic₂₅₁	—	2	2	no	—
168	C₂×Dic₂₅₁	—	2	1	no	—
169	C₂×Dic₂₅₁	C₂×D₄	1	1	yes	characteristic
170	C₂×Dic₂₅₁	C₂×D₄	1	1	yes	characteristic
171	C₄×D₂₅₁	—	2	4	no	—
172	C₄×D₂₅₁	—	2	4	no	—
173	C₄×D₂₅₁	—	2	2	no	—
174	C₄×D₂₅₁	—	2	4	no	—
175	C₄×D₂₅₁	—	2	1	no	—
176	C₄×D₂₅₁	—	2	1	no	—
177	C₄×D₂₅₁	—	2	2	no	—
178	C₄×D₂₅₁	—	4	2	no	—
179	C₄×D₂₅₁	C₂×D₄	1	2	yes	—
180	C₄×D₂₅₁	C₂×D₄	1	2	yes	—
181	C₂₅₁⋊C₈	—	2	1	no	—
182	C₂₅₁⋊C₈	—	2	1	no	—
183	C₂³×C₂₅₁	—	2	1	no	—
184	C₂³×C₂₅₁	—	2	1	no	—
185	C₂³×C₂₅₁	C₂×D₄	1	1	yes	characteristic
186	Q₈×C₂₅₁	—	2	1	no	—
187	Q₈×C₂₅₁	C₂×D₄	1	2	yes	complemented
188	D₄×C₂₅₁	—	2	4	no	—
189	D₄×C₂₅₁	—	2	1	no	—
190	D₄×C₂₅₁	—	2	1	no	—
191	D₄×C₂₅₁	—	2	1	no	—
192	D₄×C₂₅₁	—	4	2	no	—
193	D₄×C₂₅₁	C₂×D₄	1	2	yes	complemented
194	C₂×C₄×C₂₅₁	—	2	4	no	—
195	C₂×C₄×C₂₅₁	—	2	1	no	—
196	C₂×C₄×C₂₅₁	—	2	1	no	—
197	C₂×C₄×C₂₅₁	—	2	1	no	—
198	C₂×C₄×C₂₅₁	—	2	1	no	—
199	C₂×C₄×C₂₅₁	C₂×D₄	1	1	yes	characteristic
200	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
201	C₈×C₂₅₁	—	2	1	no	—
202	C₈×C₂₅₁	—	2	1	no	—
203	C₂²×C₂₅₁	—	2	1	no	—
204	C₂²×C₂₅₁	—	2	2	no	—
205	C₂²×C₂₅₁	—	2	1	no	—
206	C₂²×C₂₅₁	—	2	1	no	—
207	C₂²×C₂₅₁	—	4	1	no	—
208	C₂²×C₂₅₁	—	4	1	no	—
209	C₂²×C₂₅₁	—	4	1	no	—
210	C₂²×C₂₅₁	—	4	1	no	—
211	C₂²×C₂₅₁	—	4	1	no	—
212	C₂²×C₂₅₁	C₂²×D₄	1	1	yes	characteristic
213	C₂×D₂₅₁	—	2	1	no	—
214	C₂×D₂₅₁	—	2	2	no	—
215	C₂×D₂₅₁	—	2	1	no	—
216	C₂×D₂₅₁	—	2	1	no	—
217	C₂×D₂₅₁	—	4	1	no	—
218	C₂×D₂₅₁	—	4	1	no	—
219	C₂×D₂₅₁	—	4	4	no	—
220	C₂×D₂₅₁	—	4	8	no	—
221	C₂×D₂₅₁	—	4	1	no	—
222	C₂×D₂₅₁	—	4	1	no	—
223	C₂×D₂₅₁	—	4	1	no	—
224	C₂×D₂₅₁	—	8	4	no	—
225	C₂×D₂₅₁	#120	1	2	yes	—
226	C₂×D₂₅₁	#135	1	2	yes	—
227	C₂×D₂₅₁	AGL(1,ℤ/8)	1	2	yes	—
228	C₄×C₂₅₁	—	2	1	no	—
229	C₄×C₂₅₁	—	2	2	no	—
230	C₄×C₂₅₁	—	4	1	no	—
231	C₄×C₂₅₁	C₂²×D₄	1	1	yes	characteristic
232	C₄×C₂₅₁	C₂²×D₄	1	1	yes	characteristic
233	Dic₂₅₁	—	2	1	no	—
234	Dic₂₅₁	—	2	2	no	—
235	Dic₂₅₁	—	4	1	no	—
236	Dic₂₅₁	#120	1	2	yes	—
237	C₂×C₂₅₁	—	4	1	no	—
238	C₂×C₂₅₁	—	4	2	no	—
239	C₂×C₂₅₁	—	8	1	no	—
240	C₂×C₂₅₁	C₂×#120	1	1	yes	characteristic
241	C₂×C₂₅₁	C₂×#135	1	1	yes	characteristic
242	C₂×C₂₅₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
243	D₂₅₁	—	4	1	no	—
244	D₂₅₁	—	4	2	no	—
245	D₂₅₁	—	8	1	no	—
246	D₂₅₁	#449	1	4	yes	direct product factor
247	C₂₅₁	C₂×#449	1	1	yes	characteristic, complemented, Sylow
248	C₂×#449	—	251	1	no	maximal, Sylow
249	C₂²×#41	—	251	1	no	—
250	C₂²×SD₁₆	—	251	1	no	—
251	C₂²×D₈	—	251	1	no	—
252	C₂×#121	—	251	1	no	—
253	#449	—	251	1	no	—
254	#449	—	251	1	no	—
255	#449	—	251	1	no	—
256	#449	—	251	1	no	—
257	#449	—	251	1	no	—
258	#449	—	251	1	no	—
259	#449	—	251	1	no	—
260	#449	D₂₅₁	1	1	yes	characteristic, direct product factor
261	C₂×#103	—	251	1	no	—
262	C₂×#102	—	251	1	no	—
263	C₂×C₂²⋊C₈	—	251	1	no	—
264	C₂×#41	—	502	1	no	—
265	C₂×#41	—	502	4	no	—
266	C₂×#41	—	502	4	no	—
267	C₂×#41	—	502	1	no	—
268	C₂×#41	—	251	1	no	—
269	C₂×#41	—	251	1	no	—
270	C₂×#41	—	251	1	no	—
271	C₂×#41	C₂×D₂₅₁	1	1	yes	characteristic, complemented
272	C₂²×Q₈	—	251	1	no	—
273	C₂²×D₄	—	502	1	no	—
274	C₂²×D₄	—	502	1	no	—
275	C₂²×D₄	—	251	1	no	—
276	C₂²×D₄	—	251	1	no	—
277	C₂³×C₄	—	502	1	no	—
278	C₂³×C₄	—	251	1	no	—
279	C₂×SD₁₆	—	502	4	no	—
280	C₂×SD₁₆	—	251	1	no	—
281	C₂×SD₁₆	—	251	1	no	—
282	C₂×SD₁₆	—	251	1	no	—
283	C₂×SD₁₆	C₂×D₂₅₁	1	1	yes	characteristic, complemented
284	C₂×D₈	—	502	4	no	—
285	C₂×D₈	—	251	1	no	—
286	C₂×D₈	—	251	1	no	—
287	C₂×D₈	—	251	1	no	—
288	C₂×D₈	C₂×D₂₅₁	1	1	yes	characteristic, complemented
289	C₂²×C₈	—	251	1	no	—
290	C₂²×C₈	—	251	1	no	—
291	#121	—	502	1	no	—
292	#121	—	502	1	no	—
293	#121	—	251	1	no	—
294	#121	—	251	1	no	—
295	#121	—	251	1	no	—
296	#121	C₂×D₂₅₁	1	1	yes	characteristic, complemented
297	C₂×C₄⋊C₄	—	251	1	no	—
298	C₂×C₂²⋊C₄	—	502	1	no	—
299	#103	—	251	1	no	—
300	#103	—	251	1	no	—
301	#103	—	251	1	no	—
302	#103	C₂×D₂₅₁	1	1	yes	characteristic, complemented
303	#102	—	251	1	no	—
304	#102	—	251	1	no	—
305	#102	—	251	1	no	—
306	#102	C₂×D₂₅₁	1	1	yes	characteristic, complemented
307	C₂²⋊C₈	—	251	1	no	—
308	C₂²⋊C₈	—	251	1	no	—
309	C₂²⋊C₈	—	251	1	no	—
310	C₂²⋊C₈	C₂×D₂₅₁	1	1	yes	characteristic, complemented
311	C₂⁴	—	502	1	no	—
312	C₂⁴	—	502	1	no	—
313	C₂⁴	—	251	1	no	—
314	#41	—	2	2	no	—
315	#41	—	2	2	no	—
316	#41	—	502	8	no	—
317	#41	—	502	2	no	—
318	#41	—	502	2	no	—
319	#41	—	502	8	no	—
320	#41	—	502	2	no	—
321	#41	—	502	2	no	—
322	#41	—	502	2	no	—
323	#41	—	502	2	no	—
324	C₂×Q₈	—	502	1	no	—
325	C₂×Q₈	—	502	2	no	—
326	C₂×Q₈	—	251	4	no	—
327	C₂×Q₈	—	251	1	no	—
328	C₂×Q₈	C₂²×D₂₅₁	1	1	yes	characteristic
329	C₂×D₄	—	2	1	no	—
330	C₂×D₄	—	2	1	no	—
331	C₂×D₄	—	1004	4	no	—
332	C₂×D₄	—	502	1	no	—
333	C₂×D₄	—	502	1	no	—
334	C₂×D₄	—	502	8	no	—
335	C₂×D₄	—	502	1	no	—
336	C₂×D₄	—	502	1	no	—
337	C₂×D₄	—	502	1	no	—
338	C₂×D₄	—	502	1	no	—
339	C₂×D₄	—	502	2	no	—
340	C₂×D₄	—	502	2	no	—
341	C₂×D₄	—	502	2	no	—
342	C₂×D₄	—	502	1	no	—
343	C₂×D₄	—	502	1	no	—
344	C₂×D₄	—	251	4	no	—
345	C₂×D₄	—	251	1	no	—
346	C₂×D₄	—	251	1	no	—
347	C₂×D₄	C₂²×D₂₅₁	1	1	yes	characteristic
348	C₂×D₄	C₂²×D₂₅₁	1	1	yes	characteristic
349	C₂²×C₄	—	2	1	no	—
350	C₂²×C₄	—	502	1	no	—
351	C₂²×C₄	—	502	8	no	—
352	C₂²×C₄	—	502	1	no	—
353	C₂²×C₄	—	502	1	no	—
354	C₂²×C₄	—	502	2	no	—
355	C₂²×C₄	—	502	2	no	—
356	C₂²×C₄	—	502	1	no	—
357	C₂²×C₄	—	502	1	no	—
358	C₂²×C₄	—	251	1	no	—
359	C₂²×C₄	—	251	1	no	—
360	C₂²×C₄	—	251	1	no	—
361	C₂²×C₄	—	251	1	no	—
362	C₂²×C₄	—	251	1	no	—
363	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
364	SD₁₆	—	2	2	no	—
365	SD₁₆	—	502	2	no	—
366	SD₁₆	—	502	2	no	—
367	SD₁₆	—	502	2	no	—
368	D₈	—	2	2	no	—
369	D₈	—	502	2	no	—
370	D₈	—	502	2	no	—
371	D₈	—	502	2	no	—
372	C₂×C₈	—	502	2	no	—
373	C₂×C₈	—	502	2	no	—
374	C₂×C₈	—	251	1	no	—
375	C₂×C₈	—	251	1	no	—
376	C₂×C₈	C₂²×D₂₅₁	1	1	yes	characteristic
377	C₂×C₈	C₂²×D₂₅₁	1	1	yes	characteristic
378	C₄⋊C₄	—	502	1	no	—
379	C₄⋊C₄	—	251	1	no	—
380	C₄⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
381	C₂²⋊C₄	—	2	1	no	—
382	C₂²⋊C₄	—	502	1	no	—
383	C₂²⋊C₄	—	502	1	no	—
384	C₂²⋊C₄	—	502	1	no	—
385	C₂³	—	2	1	no	—
386	C₂³	—	2	1	no	—
387	C₂³	—	1004	2	no	—
388	C₂³	—	1004	2	no	—
389	C₂³	—	1004	2	no	—
390	C₂³	—	1004	2	no	—
391	C₂³	—	1004	2	no	—
392	C₂³	—	502	2	no	—
393	C₂³	—	502	4	no	—
394	C₂³	—	502	2	no	—
395	C₂³	—	502	2	no	—
396	C₂³	—	502	1	no	—
397	C₂³	—	502	1	no	—
398	C₂³	—	251	1	no	—
399	C₂³	—	251	1	no	—
400	C₂³	D₄×D₂₅₁	1	1	yes	characteristic
401	Q₈	—	2	1	no	—
402	Q₈	—	502	4	no	—
403	Q₈	—	502	1	no	—
404	Q₈	—	251	2	no	—
405	Q₈	D₄×D₂₅₁	1	2	yes	complemented
406	D₄	—	2	4	no	—
407	D₄	—	2	1	no	—
408	D₄	—	2	1	no	—
409	D₄	—	2	1	no	—
410	D₄	—	4	2	no	—
411	D₄	—	1004	2	no	—
412	D₄	—	1004	2	no	—
413	D₄	—	1004	2	no	—
414	D₄	—	1004	2	no	—
415	D₄	—	502	4	no	—
416	D₄	—	502	4	no	—
417	D₄	—	502	4	no	—
418	D₄	—	502	4	no	—
419	D₄	—	502	1	no	—
420	D₄	—	502	1	no	—
421	D₄	—	502	1	no	—
422	D₄	—	251	2	no	—
423	D₄	D₄×D₂₅₁	1	2	yes	complemented
424	C₂×C₄	—	2	4	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	1004	2	no	—
430	C₂×C₄	—	502	4	no	—
431	C₂×C₄	—	502	4	no	—
432	C₂×C₄	—	502	2	no	—
433	C₂×C₄	—	502	4	no	—
434	C₂×C₄	—	502	2	no	—
435	C₂×C₄	—	502	1	no	—
436	C₂×C₄	—	502	4	no	—
437	C₂×C₄	—	502	1	no	—
438	C₂×C₄	—	502	2	no	—
439	C₂×C₄	—	502	1	no	—
440	C₂×C₄	—	502	1	no	—
441	C₂×C₄	—	251	1	no	—
442	C₂×C₄	—	251	1	no	—
443	C₂×C₄	—	251	2	no	—
444	C₂×C₄	—	251	2	no	—
445	C₂×C₄	D₄×D₂₅₁	1	1	yes	characteristic
446	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
447	C₈	—	2	1	no	—
448	C₈	—	2	1	no	—
449	C₈	—	502	1	no	—
450	C₈	—	502	1	no	—
451	C₂²	—	2	1	no	—
452	C₂²	—	2	1	no	—
453	C₂²	—	2	1	no	—
454	C₂²	—	2	2	no	—
455	C₂²	—	4	1	no	—
456	C₂²	—	4	1	no	—
457	C₂²	—	4	1	no	—
458	C₂²	—	4	1	no	—
459	C₂²	—	4	1	no	—
460	C₂²	—	2008	4	no	—
461	C₂²	—	1004	8	no	—
462	C₂²	—	1004	4	no	—
463	C₂²	—	1004	1	no	—
464	C₂²	—	1004	1	no	—
465	C₂²	—	1004	1	no	—
466	C₂²	—	1004	1	no	—
467	C₂²	—	1004	1	no	—
468	C₂²	—	502	1	no	—
469	C₂²	—	502	1	no	—
470	C₂²	—	502	1	no	—
471	C₂²	—	502	2	no	—
472	C₂²	—	251	2	no	—
473	C₂²	—	251	2	no	—
474	C₂²	—	251	2	no	—
475	C₂²	C₂×D₄×D₂₅₁	1	1	yes	characteristic
476	C₄	—	2	1	no	—
477	C₄	—	2	2	no	—
478	C₄	—	4	1	no	—
479	C₄	—	1004	1	no	—
480	C₄	—	502	1	no	—
481	C₄	—	502	2	no	—
482	C₄	—	251	2	no	—
483	C₄	C₂×D₄×D₂₅₁	1	1	yes	characteristic
484	C₄	C₂×D₄×D₂₅₁	1	1	yes	characteristic
485	C₂	—	4	1	no	—
486	C₂	—	4	2	no	—
487	C₂	—	8	1	no	—
488	C₂	—	2008	1	no	—
489	C₂	—	1004	2	no	—
490	C₂	—	1004	1	no	—
491	C₂	—	251	4	no	—
492	C₂	#120×D₂₅₁	1	1	yes	characteristic
493	C₂	#135×D₂₅₁	1	1	yes	characteristic
494	C₂	AGL(1,ℤ/8)×D₂₅₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₂₅₁
commutator, cosocle	C₂×C₄×C₂₅₁	C₂⁴
Frattini	C₂×C₄	C₂³×D₂₅₁
Fitting	#449×C₂₅₁	C₂
socle	C₂²×C₂₅₁	C₂²×D₄
hypercenter	#449	D₂₅₁
hypocenter	C₂₅₁	C₂×#449
LCS	G ▷ C₂×C₄×C₂₅₁ ▷ C₂×C₂₅₁ ▷ C₂₅₁
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #449

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×#41×D₂₅₁	C₂	semidirect
2. C₂×SD₁₆×D₂₅₁	C₂	semidirect
3. C₂×D₈×D₂₅₁	C₂	semidirect
4. #121×D₂₅₁	C₂	semidirect
5. #30631835	C₂	semidirect
6. #30631834	C₂	semidirect
7. #30631833	C₂	semidirect
8. #30631832	C₂	semidirect
9. #30631831	C₂	semidirect
10. #30631830	C₂	semidirect
11. #30631829	C₂	semidirect
12. #103×D₂₅₁	C₂	semidirect
13. #102×D₂₅₁	C₂	semidirect
14. C₂²⋊C₈×D₂₅₁	C₂	semidirect
15. #449×C₂₅₁	C₂	semidirect
16. C₂×#16860811	C₂²	semidirect
18. C₂×#16860810	C₂²	semidirect
20. C₂×#16860809	C₂²	semidirect
30. C₂×#16860799	C₂²	semidirect
31. C₂×#16860798	C₂²	semidirect
32. C₂×#16860797	C₂²	semidirect
34. C₂×D₂₀₀₈	C₂²	semidirect
35. C₂×#16860795	C₂²	semidirect
36. C₂×#16860795	C₂²	semidirect
40. #22548690	C₂²	semidirect
41. #22548689	C₂²	semidirect
44. #22548686	C₂²	semidirect
47. #22548640	C₂²	semidirect
48. #22548639	C₂²	semidirect
49. #22548638	C₂²	semidirect
50. #22548637	C₂²	semidirect
51. #22548636	C₂²	semidirect
52. #22548635	C₂²	semidirect
53. C₂²⋊(C₂₅₁⋊C₈)	C₂²	semidirect
54. (C₂×D₂₅₁)⋊C₈	C₂²	semidirect
55. (C₂×D₂₅₁)⋊C₈	C₂²	semidirect
56. C₂×#41×C₂₅₁	C₂²	semidirect
57. C₂×SD₁₆×C₂₅₁	C₂²	semidirect
58. C₂×D₈×C₂₅₁	C₂²	semidirect
59. #121×C₂₅₁	C₂²	semidirect
60. #103×C₂₅₁	C₂²	semidirect
61. #102×C₂₅₁	C₂²	semidirect
62. C₂²⋊C₈×C₂₅₁	C₂²	semidirect
77. Q₈×D₂₅₁	D₄	semidirect
93. D₄×D₂₅₁	D₄	semidirect
152. Dic₅₀₂	C₂×D₄	semidirect
158. D₁₀₀₄	C₂×D₄	semidirect
187. Q₈×C₂₅₁	C₂×D₄	semidirect
193. D₄×C₂₅₁	C₂×D₄	semidirect
246. D₂₅₁	#449	direct (N × H)
247. C₂₅₁	C₂×#449	semidirect
260. #449	D₂₅₁	direct (N × H)
271. C₂×#41	C₂×D₂₅₁	semidirect
283. C₂×SD₁₆	C₂×D₂₅₁	semidirect
288. C₂×D₈	C₂×D₂₅₁	semidirect
296. #121	C₂×D₂₅₁	semidirect
302. #103	C₂×D₂₅₁	semidirect
306. #102	C₂×D₂₅₁	semidirect
310. C₂²⋊C₈	C₂×D₂₅₁	semidirect
405. Q₈	D₄×D₂₅₁	semidirect
423. D₄	D₄×D₂₅₁	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×#41×D₂₅₁	2
C₂×SD₁₆×D₂₅₁	2
C₂×D₈×D₂₅₁	2
#121×D₂₅₁	2
#30631835	2
#30631834	2
#30631833	2
#30631832	2
#30631831	2
#30631830	2
#30631829	2
#103×D₂₅₁	2
#102×D₂₅₁	2
C₂²⋊C₈×D₂₅₁	2
#449×C₂₅₁	2
C₂×#449	251

Subgroups — #449×D251 #44559562

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #449×D₂₅₁ #44559562